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New Conditions for the Existence of Infinitely Many Solutions for a Quasi-Linear Problem

Part of: Elliptic equations and systems Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  15 December 2015

Francesca Faraci  and
Csaba Farkas
Francesca Faraci
Affiliation:
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 95125 Catania, Italy ([email protected])
Csaba Farkas
Affiliation:
Fcaultatea de Matematică şi Informatică, Universitatea Babeş-Bolyai Cluj-Napoca, Str. Mihail Kogalniceanu nr. 1, 400084, Cluj-Napoca, Romania ([email protected])
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Abstract

In this paper we study a quasi-linear elliptic problem coupled with Dirichlet boundary conditions. We propose a new set of assumptions ensuring the existence of infinitely many solutions.

Keywords

p-Laplacianinfinitely many solutionsDirichlet problemvariational methods

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 35J92: Quasilinear elliptic equations with $p$-Laplacian 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 655 - 669
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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